fresh air, as in outside air, is the best air for your plants.. nothing can beat it... plentiful supply of co2 for the plants... constantly changing itself over.. what else could you ask for?
but it isnt VITAL to growing to have it...
as long as you have good air movement.. be it a box fan or two or an oscilating fan....
some sorta of air exchange... an open door works.. your plants just need new air from somewhere
and you dont have heat build up issues, then imho you will be fine in the storage room...
ideally you want to get fresh outside air to your indoor garden somehow, but your plants can grow just fine without it... assuming you meet the above criteria..
good luck
sampson